families as shocks - university of pennsylvania school of ...vr0j/slides/slvenezia.pdf · 2.f...

Families as Shocks

Luis CubedduIMF

Jose-Vıctor Rıos-RullPenn, CAERP, CEPR

August 21, 2002

EEA Meetings, Venezia, August 2002

1. Introduction

•There is a large literature both in macro and in applied micro (consumption,savings, labor) that considers shocks to earnings or to employment status asthe major source of differential outcomes across households (under incompleteinsurance markets).

•But there are other events in people’s lives that can also be thought as playinga major role in shaping the economic performance of people, and, in particular,their consumption and savings. I am thinking of marital status (another one,health, mostly affects earnings).

•Shocks to earnings do not seem to change the total size of wealth much: Aiyagari(1994) measured the size of precautionary savings to be under 10% of savings.More recently, Castaneda et al. (2002) have found that that shocks to earningsincrease wealth by 5.5%.

EEA Meetings, Venezia, August 2002 1

1. The Plan

•Today I want to argue that the type of family structure in which an individuallives and its changes over time play a major role in shaping economic decisions.

•I will do it in a very simple manner. Even though we know that peoplechoose which type of family arrangement to live in, I will treat family type as anexogenous event, as a shock, generated by a stochastic process and I will showhow dramatically different are the implications of different stochastic processesfor the economic outcomes that macroeconomists are interested in, such as theevolution of savings.

•For this we need a growth model with agents and households being differentthings. Let’s build one.


2. The Model

We use an Overlapping Generations Model. Agents are indexed by:

•Age: i ∈ {1, 2, · · · , I}. Time ages people: i′ = i + 1.

•Sex: g ∈ {m, f}, (g∗ is spouse’s gender). Sex of agents does not change:g′ = g.

•Marital Status: z ∈ {so, sw, 1, 2, · · · , I}, (Single without and with dependentsand the spouse’s age). This we think of a shock: with πi,g(z′|z) being theprobability of moving to state z′, conditional on being in state z.

•Assets: a ∈ A. These assets are attached to the household and it varies bothbecause of savings and because of changes in the composition of the household.


2.a Simplest Demographics

• Constant population, no early death

µi+1,g,z′ =∑

z

πi,g(z′|z) µi,g,z

– µi,g,z : Measure of people of type {i, g, z}.

• Consistency of demographic conditions (measure age i males married to age jfemales equals measure age j females married to age i males).

µi,m,j = µj,f,i


2.b Preferences and Endowments

•Preferences of an age 1 individual. E{∑I

i=1 βi−1 ui,z(c)}

•Household type affects consumption (equivalence scales): ui,z(c) = u(

cηi,z

).

(no time allocation or fertility decisions).

•Labor earnings endowment: εi,g,z. For most of today’s marital status does notaffect earnings: εi,g,z = εi,g for all z ∈ Z.

2.c Markets

•No insurance for changes in marital status nor life insurance. (perhaps there isa lot of moral hazard).

•No borrowing possibilities (not very important).


2.d Marital Property Status

•We assume common property of all household assets, no memory of who broughtwhat to the household.

•This is not necessarily the law of all countries but it is the de facto system formost people, those with few assets, or those with small differences in assets atthe time of marriage.

•An important question is the extent to which property can be protected (e.g.young people save mostly in the form of human capital that is typically non–transferable).


2.e Single Agent’s Problem: z ∈ {so, sw}

vi,g,z(a) = maxc≥0,y∈A

ui,g,z(c) + β E{vi+1,g,z′(a′)|z} s.t.

c + y = (1 + r) a + w εi,g,z

a′ = y if z′ ∈ {so, sw}

a′ = y + Az′,g∗ if z′ ∈ {1, .., I}

•Az′,g∗ : Assets spouse brings into marriage. (Random variable).

•Agent must know asset distribution of prospective partners.


2.f Married Couple’s Problem: z ∈ {1, .., I}

•We need to specify a bunch of details of how the family is organized and of howthe decisions are made. The choices that we made are

1. Spouses are constrained to enjoy equal consumption.

2. Subject to common property regime (assets cannot be traced to its originalowner).

3. The household solves a joint maximization problem with weights: ξi,m,j =1− ξj,f,i.

4. Upon divorce, assets are divided

• ψi,g,j : fraction of assets to {i, g, j}• ψj,g∗,i : fraction of assets to spouse.• May add to less than 1 because of divorce costs.


2.g Married Couple’s Problem: z ∈ {1, .., I} cont.

maxc≥0,y∈A

ui,g,j(c) + β ξi,g,jE{vi+1,g,z′g(a′g)|j} + β ξj,g∗,i E{vj+1,g∗,z′

g∗(a′g∗)|i}

c + y = (1 + r) a + w(εi,g,j + εj,g∗,i)

•if no divorce: a′g = a′g∗ = y.

•if divorce and no remarriage:

{a′g = ψi,g,j y,a′g∗ = ψj,g∗,i y.

•if divorce and remarriage

{a′g = ψi,g,j y + Az′g,g∗,

a′g∗ = ψj,g∗,i y + Azg∗,g.


2.h Equilibrium

•We look at stationary situations where the key Equilibrium object, φi,g,z, is aprobability measure on assets:

•φi,g,z(B) µi,g,z : Measure of agents type {i, g, z} with assets in B.

Equilibrium requires that agents solve their problem given factor prices anddistribution of wealth φ, and that there is consistency of wealth distribution andindividual behavior:

φi+1,g,z′(B) =∑

z∈Z

πi,g(z′|z)∫

a∈Aχa′i,g,z(a)∈B φi,g,z(da)

where χ is the indicator function.


3. A baseline economy without demographic change

•No early mortality, no population growth, no productivity growth.

•One half of the population starts married to people of their own age. They havean age dependent number of children that peaks at age 43.

•The other half starts single, a quarter with and a quarter without dependents.Those that have dependents have one. The lack of change over time makes allsingles look in many ways identical.

•There is no further demographic change. This is like a standard economywithout marital considerations.

•Marital status does not affect earnings.

•There are economies of scale in consumption.

•Calibrated to a wealth to output ratio of 4.15 and NIPA. Interest rate is 2.48%.


20 30 40 50 60 70 800

20

40

60

80

100

Age

Perc

ent

Population Measure (Male, No Change−Baseline)

MarriedSingle w/o DepSingle w/ Dep


20 30 40 50 60 70 800

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Age

Earn

ings

Earnings (per person) No Change−Baseline

Married Single Males Single Females


20 30 40 50 60 70 800

0.5

1

1.5

2

2.5

3

Age

Ass

etAssets (per person) (Overall, No Change−Baseline)

Married All Single Males All Single Females


Other economies with changes in marital status

• 2. An economy where all people start as singles (half with and half withoutdependents) and they all marry at age 47 (there is no divorce and the samemarriages as in base).

• 3. An economy where all people start married and they all divorce. One half endsup with dependents and one half without. Females keep 60% of assets, andmales 40%.

• 4. An economy where all people alternate, being one period married and onesingle (again 50% married, 25% singles with and 25% without).

• 5. An economy where marital status is i.i.d.

• 6. An economy like the U.S. in the nineties.


Population Structure

20 40 60 800

20

40

60

80

100

Per

cent

1. Base

Married Single w/o DepSingle w/ Dep

20 40 60 800

50

100

2. Late Mar

20 40 60 800

50

100

3. Late Div

20 40 60 800

50

100

Per

cent

Age

4. Altern

20 40 60 800

50

100

Age

5. IID

20 40 60 800

50

100

Age

6. 90s


What are their macroeconomic properties?Economy Wealth W/Y r

1. Base 4.15 4.15 2.48%

2. Late Marriage 2.76 3.13 4.73%

3. Late Divorce 5.00 4.65 1.57%

4. Alternation 1.28 1.67 10.1%

5. i.i.d. Marital Status 2.66 3.01 4.95%

6. U.S. in the nineties – 3.24 4.54%

•Huge differences in assets holdings. These are general equilibrium effects; partialequilibrium effects are much larger.

•Future marriages are serious disincentives to save, especially later in life: therate of return is negative.

•Late divorce are incentives to save. Females’ lower earnings and higher share ofassets makes them want to save (equal weights in decisions).

•Turnover lowers savings but not always. The effects are big.


Asset Holdings of Households

20 40 60 800

1

2

3

Perc

ent

1. Base

20 40 60 800

1

2

3

2. Late Mar

20 40 60 800

1

2

3

3. Late Div

20 40 60 800

0.5

1

1.5

2

2.5

3

3.5

Perc

ent

Age

4. Altern


20 40 60 800

1

2

3

Age

5. IID

20 40 60 800

1

2

3

Age

6. 90s


Asset Holdings of Males

20 40 60 800

1

2

3

Perc

ent

1. Base

20 40 60 800

1

2

3

2. Late Mar

20 40 60 800

1

2

3

3. Late Div

20 40 60 800

0.5

1

1.5

2

2.5

3

3.5

Perc

ent

Age

4. Altern


20 40 60 800

1

2

3

Age

5. IID

20 40 60 800

1

2

3

Age

6. 90s


Assets Holdings of Females

20 40 60 800

1

2

3

Perc

ent

1. Base

20 40 60 800

1

2

3

2. Late Mar

20 40 60 800

1

2

3

3. Late Div

20 40 60 800

0.5

1

1.5

2

2.5

3

3.5

Perc

ent

Age

4. Altern


20 40 60 800

1

2

3

Age

5. IID

20 40 60 800

1

2

3

Age

6. 90s


Age profile of saving rates

20 40 600

0.1

0.2

0.3

0.4

Savi

ng R

ate

1. Base

20 40 600

0.1

0.2

0.3

0.4

2. Late Mar

20 40 600

0.1

0.2

0.3

0.4

3. Late Div

20 40 600

0.1

0.2

0.3

0.4

Savi

ng R

ate

Age

4. Altern

20 40 600

0.1

0.2

0.3

0.4

Age

5. IID

20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

Age

6. 90s



Asset destruction when divorce

Economy Wealth W/Y Destr r

1. Base 4.15 4.15 0.000 2.48%

2. Late Marriage 2.76 3.13 0.000 4.73%

3. Late Divorce 3.80 3.91 0.044 2.93%

4. Alternation 0.81 1.11 0.047 10.09%

5. i.i.d. Marital Status 1.76 2.21 0.046 7.70%

6. U.S. in the nineties – 3.13 0.006 4.87%

•Asset destruction reduces a lot assets.

•It can be a large chunk of GDP (1.%).

•Makes all changes in marital status reduce savings.


Conclusion

•I wanted to raise the issue that household composition is important even formacroeconomic questions.

•Its importance is quantitative.

•We should build models where we account explicitly for household composition,this is families.

•Of course we should model the decision of how individuals choose their familyand build it into macroeconomic models. (Regalia and Rıos-Rull (2001), and alot of Raquel Fernandez and her coauthors’ work).


families as shocks - university of pennsylvania school of ...vr0j/slides/slvenezia.pdf · 2.f...

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